In set-builder form,the empty set is represented by

Examine whether the following statement is true or false:
$\{a, e\} \subset \{x : x \text{ is a vowel in the English alphabet}\}$

If a set $A$ has $n$ elements,then the total number of subsets of $A$ is

If $Q = \{x : x = \frac{1}{y}, y \in N\}$,then which of the following is true?

Let $S = \{1, 2, 3, \ldots, n\}$ and $A = \{(a, b) \mid 1 \leq a, b \leq n\} = S \times S$. $A$ subset $B$ of $A$ is said to be a good subset if $(x, x) \in B$ for every $x \in S$. Then,the number of good subsets of $A$ is

Determine the subset for the set $\{n(n+1)(2n+1) : n \in \mathbb{Z}\}$.